Power plant instrumentation and control handbook : A guide to thermal power plants

Power Plant Instrumentation

and Control Handbook

A Guide to Thermal Power Plants

Swapan Basu

Systems & Controls Kolkata, India

Ajay Kumar Debnath

Systems & Controls Kolkata, India

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Dedication

This book is dedicated to the promising and growing engineers

working in/around or studying thermal power plant

instrumentation and control systems who can render services

to mankind by providing sparse, pollution-free energy

for human progression.

Foreword

With the advent of technological advancement in all the

fields, knowledge and know-how are now available, in bits

and pieces, with just a click of the mouse, on the computer.

However, it can be time-consuming to find the desired in￾formation in a consolidated manner, or it may be difficult to

find the exact subject information required.

Modern power plant engineering is a vast subject with

different fields of application for all branches of technol￾ogy. In this book, the authors have included their experi￾ences from a different angle focusing on instrumentation

and control systems.

There are number of valuable books available on power

plants covering different subjects, but there is a dearth of

a single volumes incorporating the majority of the equip￾ment in relation to the process. The chapters of this book

cover various subjects on the process and associated

instrumentation with alternative arrangements (if any). The

text is well demonstrated with facts and figures that make

this book easy to understand.

In general, this book accentuates both subcritical and

supercritical plants, and there are separate appendices

covering supercritical plants as well the emerging demand

for the higher efficiency and lower pollution aspects of

subcritical plants.

The authors worked for decades with leading consulting

firms in India and abroad and keep in touch with modern

technology. I truly feel that their experiences will greatly

benefit both practicing engineers and students of power

plant engineering.

I wish every success to the authors of this book.

S. K. Sen

ix

Preface

Technical books that have theoretical and practical ap￾proaches are available worldwide about several subsystems

of thermal power plant instrumentation and controls. This

book endeavors to act as a way to balance two extreme

lines of thinking, giving a comprehensive approach to

plants’ measurements and controls.

What is here is primarily meant for professionals

working with thermal power plant instrumentation and

control systems. Budding (fresh) engineers who start their

careers in thermal power plant instrumentation and control

engineering, and those practicing professionals of other

disciplines, will greatly benefit from the comprehensive￾ness and practical approaches in this book. It will be a very

good reference for engineering students who are pursuing

higher-level studies in various branches of engineering.

Highly developed and advanced mathematical de￾ductions are passed up as much as possible; instead phys￾ical explanations have been given so that readers get a

proper feel of the system so that the book could be kept

within a very limited dimension. The text part incorporates

an abridged description on the subject being dealt with

along with relevant figures and tables to visually show a

clear picture of it. In all cases, detailed specifications of the

instruments, subsystems, and systems have been included

in addition to practical control loops and logistics to enable

the book to be “all-time companion” for practicing

engineers.

Discussions about both subcritical and super-ultra su￾percritical power plants, as well as IGCCs, have been

included in order to take a look at future trends in power

plants. Content keeps pace with development work in the

field of electronics and control and communication engi￾neering, with special attention to inclusion of the means

and methods of system integration with fieldbus systems,

OPC servers, and so on. Application of artificial intelli￾gence and fuzzy logic in power plant instrumentation have

been covered in detail.

In an attempt to incoporate this extensive subject area

into the form of a book, the authors have carried out a great

deal of research over years so as to include the knowledge

gained during their decades-long global experience in

thermal power plant instrumentation engineering. We wish

to convey our sincere thanks to the companies who

entrusted us to work in this specialized area of engineering.

The authors feel rewarded only when their research work is

able to benefit future engineers who can serve the global

population by providing scarce pollution-free energy for

human development.

Swapan Basu

Ajay Kumar Debnath

xi

Acknowledgments

At the outset, the authors wish to extend their gratitude to their

professors of their engineering institutiondBengal Engi￾neering College, Sibpore (now IIEST)dand their power plant

and instrumentation gurus: the late Samir Kumar Shome

(former DCL) and the late Makhan Lal Chakraborty (former

DCL) for their great teaching in this area. The authors are

extremely indebted to Dr. Shankar Sen (former professor at B.

E.College) for his encouragement during development the

book. While working on the book we were supported with

information and suggestions of former colleagues D. K.

Sarkar, J. K. Sarkar, D. J. Gupta, S. Chakraborty, A. Thakur,

and Arijit Ghosh. In addition, we convey sincere thanks to

friends: A. Bhattachariya (Kolkata), A. Sarkar (Norway),

A. Tendulkar (Mumbai), N. Kirloskar (Pune), and

S. Mohanty (Gurgaon) for their support and sharing of

technical information. We would like to thank the authors of

the works mentioned throughout the book and the Internet

documents that stimulated and helped us write this book. The

authors also like to thank the entire team of Systems &

Controls Kolkata for infrastructural support. The authors

would like to thank the entire team at Elsevier, the publisher,

who took all the pains to bring it through to publication.

Last but not the least, we would like to thank our

children Idai(Raj), Piku(Deb), Arijita, and Arijit for their

continuous inspiration and support. A special thanks to our

wives, Bani Basu and Syama Debnath, for managing the

family show with care and for encouraging us so that we

could dedicate time to the book. The authors sincerely

acknowledge that without all these supports it would have

been impossible to publish this book.

xiii

Chapter I

Introduction

1. INTRODUCTION

The authors of this book have been associated with the

Instrumentation and Control System of Modern Power

Plants for more than two decades while working with a

leading consulting firm. They are still in touch with modern

technology by associating with the engineering and con￾sultancy activities of ongoing projects. We wanted to

document their extended experience in the form of a

reference book so that professional engineers, working

engineers in power plants, and students could benefit from

the knowledge gathered during their tenure.

There are so many valuable and good books available

on a variety of subjects related to power plants about

boilers, turbines, and generators and their subsystems, but it

is very difficult to get a single book or single volume of a

book to cater to the equipment, accessories, or items along

with the instrumentation and control systems associated

with them. In this book, there is a very brief description of

the system and equipment along with diagrams for a

cursory idea about the entire plant. Up-to-date piping and

instrumentation diagrams (P&IDs) are included to better

understand the tapping locations of measuring and control

parameters of the plant.

Various types of instruments, along with sensors,

transmitters, gauges, switches, signal conditioner/converter,

etc., have been discussed in depth in dedicated chapters,

whereas special types of instruments are covered in sepa￾rate chapters. Instrument data sheets or specification

sheets are included so that beginners may receive adequate

support for preparing the documents required for their

daily work.

The control system chapters VIII, IX and X incorporate

the latest control philosophy that has been adopted in

several power stations.

This book mainly emphasizes subcritical boilers, but a

separate appendix is provided on supercritical boilers

because of their economic and low-pollution aspects, which

create a bigger demand and need than do conventional

subcritical boilers.

It is hoped that this book may help students and/or those

who perform power plant-oriented jobs.

2. FUNDAMENTAL KNOWLEDGE ABOUT

BASIC PROCESS

Power plant concepts are based on the Laws of Thermo￾dynamics, which depict the relationship among heat,

work, and various properties of the systems. All types

of energy transformations related to various systems

(e.g., mechanical, electrical, chemical etc.) may fall under

the study of thermodynamics and are basically founded

on empirical formulae and system and/or process

behavior. A thermodynamic system is a region in space on

control volume or mass under study toward energy

transformation within a system and transfer of energy

across the boundaries of the system.

2.0 Ideas within and Outside the System

1. Surrounding: Space and matter outside the thermody￾namic system.

2. Universe: Thermodynamic system and surroundings

put together.

3. Thermodynamic systems:

a. Closed: Only energy may cross the boundaries with

the mass remaining within the boundary.

b. Open: Transfer of mass takes place across the

boundary.

c. Isolated: The system is isolated from its surround￾ing and no transfer of mass or energy takes place

across the boundary.

4. State: It is the condition detailed in such a way that one

state may be differentiated from all other states.

5. Property: Any observable characteristics measurable in

terms of numbers and units of measurement, including

physical qualities such as pressure, temperature, flow,

level, location, speed, etc. The property of any system

depends only on the state of the system and not on the

process by which the state has been achieved.

a. Intensive: Does not depend on the mass of the sys￾tem (e.g., pressure, temperature, specific volume,

and density).

b. Extensive: Depends on the mass of the system (i.e.,

volume).

Power Plant Instrumentation and Control Handbook

Copyright © 2015 Elsevier Ltd. All rights reserved.

1

6. Specific weight: The weight density (i.e., weight per

unit volume).

7. Specific volume: Volume per unit mass.

8. Pressure: Force exerted by a system per unit area of

the system.

9. Path: Thermodynamic system passes through a series

of states.

10. Process: Where various changes of state take place.

11. Cyclic process: The process after various changes of

state complete their journey at the same initial point

of state.

2.0.1 Zeroeth Law of Thermodynamics

“If two systems are both in thermal equilibrium with a third

system, they are in thermal equilibrium with each other.”

Thermal equilibrium displays no change in the thermody￾namic coordinates of two isolated systems brought into

contact; thus, they have a common and equal thermody￾namic property called temperature. With the help of this

law, the measurement of temperature was conceived.

A thermometer uses a material’s basic property, which

changes with temperature.

2.0.1.1 Energy

“The definition in its simplest form is capacity for pro￾ducing an effect.” There are a variety of classifications for

energy.

1. Stored energy may be described as the energy contained

within the system’s boundaries. There are various

forms, such as:

a. Potential

b. Kinetic

c. Internal

2. Energy in transition may be described as energy that

crosses the system’s boundaries. There are various

types, such as:

a. Heat energy (thermal energy)

b. Electrical energy

c. Work

2.0.1.2 Work

“Work is transferred from the system during a given

operation if the sole effect external to the system can be

reduced to the rise of a weight.” This form of energy is

transferred from one system to another system originally at

different temperatures. It may take place by contact and

without mass flow across the boundaries of the two sys￾tems. This energy flows from a higher temperature to a

lower temperature and is energy in transition only and not

the property. The unit in the metric system is kcal and is

denoted by Q.

2.0.1.3 Specific Heat

Specific heat is defined as the amount of heat required to

raise the temperature of a substance of unit mass by one

degree. There are two types of specific heat:

1. At constant pressure and denoted as Cp

2. At constant volume and denoted as Cv

Heat energy is a path function and the amount of heat

transfer can be given by the following:

1Q2 ¼ Integration from T1 to T2 of m Cn dT;

i:e:; ZT2

T1

ðm Cn dTÞ;

where 1 and 2 are two points in the path through which

change takes place in the system, m is the mass, Cn is

the specific heat and maybe Cp, dT is the differential tem￾perature, and T1 and T2 are the two temperatures at point 1

and 2 of the path.

2.0.1.4 Perfect Gas

A particular gas that obeys all laws strictly under all con￾ditions is called a perfect gas. In reality no such gas exists;

however, but by applying a fair approximation some gases

are considered as perfect (air and nitrogen) and obey the

gas laws within the range of pressure and temperature of a

normal thermodynamic application.

2.0.2 Boyle’s Law and the Charles Law

2.0.2.1 Boyle’s LawdLaw I

The volume of a given mass of a perfect gas varies inversely

as the absolute pressure when temperature is constant.

2.0.2.2 Charles LawdLaw II

The volume of a given mass of a perfect gas varies directly

as the absolute temperature, if the pressure is constant.

2.0.3 General and Combined Equation

From a practical point of view, neither Boyle’s Law nor the

Charles Law is applicable to any thermodynamic system

because volume, pressure, and temperature, etc., all vary

simultaneously as an effect of others. Therefore, it is

necessary to obtain a general and combined equation for a

given mass undergoing interacting changes in volume,

pressure, and temperature:

n NT=p; when T is constant ðBoyle’s LawÞ

n NT; when p is constant ðCharles LawÞ:

Therefore, v N T/p when both pressure and temperature

vary

2 POWER PLANT INSTRUMENTATION AND CONTROL HANDBOOK

or

n ¼ k:T=p;

where k is a constant that depends on temperature scale and

properties of gas, or

pn ¼ mRT;

where m is the mass of gas and R is a constant. This

depends on temperature scale and properties of gas: p ¼ ab￾solute pressure of gas in kgf/m2

, v ¼ volume of gas in m3

,

m ¼ mass of gas in kg, and T ¼ absolute temperature of gas

in degrees K. Therefore R ¼ pV/mT ¼ kgf/m2 m3

/kg K

¼ kgf.m/kg/degree K.

R ¼ 30.26 kgf.m/kg/degree K for nitrogen

R ¼ 29.27 kgf.m/kg/per degree K for air

R ¼ 26.50 kgf.m/kg/degree K for oxygen

R ¼ 420.6 kgf.m/kg/degree K for hydrogen

2.0.3.1 Universal Gas Constant

After performing experiments, it was revealed that for

any ideal gas, the product of its characteristic gas

constant and molecular weight is a constant number and

is equal to 848. Therefore, by virtue of this revelation,

848 kgf.m/kg/degree K is called the Universal Gas

Constant.

For example: MR ¼ molecular weight in kg R

MR ¼ 29.00 29.27 z 848 for air

MR ¼ 2.016 420.6 z 848.5 for hydrogen

MR ¼ 28.016 30.26 z 847.6 for nitrogen

MR ¼ 32 26.5 z 848 for oxygen

2.0.4 Avogadro’s Law/HypothesisdLaw III

This states that the molecular weights of all the perfect

gases occupy the same volume under the same conditions

of pressure and temperature.

2.0.5 First Law of Thermodynamics

When a system undergoes a cyclic change, the algebraic

sum of work transfers is proportional to the algebraic sum

of heat transfers or work or heat is mutually convertible one

into the other.

Joules’ experiments on this subject led to an interesting

and important observation showing the net amount of heat

in kcal to be removed from the system was directly pro￾portional to the net amount of work done in kcal on the

system.

It is the convention that whenever work is done by the

system, the amount of work transfer is considered as þve,

and when work is done on the system, the amount of work

transfer is considered as ve

2.0.5.1 Internal Energy

There exists a property of a system called energy E, such

that change in its value is the algebraic sum of the heat

supplied and the work done during any change in state.

dE ¼ vQ vW

This is also described as corollary 1 of the First Law of

Thermodynamics.

Energy E may include many types of energies, such as

kinetic, potential, electric, magnetic, surface tension, etc.,

but these values, negligible considering the thermodynamic

system, are ignored and only the energy due to change in

temperature is considered. This type of energy is called

internal energy and is denoted by U.

2.0.5.2 Adiabatic Work

Whenever the change of state takes place without any heat

transfer, it is called an adiabatic process. The equation can

be written as follows:

DU ¼ Wad; Wad is the adiabatic work done

It can be established that change in internal energy DU

is independent of process path. Thus, it is evident that

adiabatic work Wad would remain the same for all adiabatic

paths between the same pair of end states.

2.0.6 Law of the Conservation of Energy

“In an isolated system, the energy of the system remains

constant.” This is known as the second corollary of the First

Law of Thermodynamics.

2.0.6.1 Constant Volume Process

The volume of the system is constant. Work done being

zero, due to heat addition to the system, there would be an

increase in internal energy or vice versa.

2.0.6.2 Constant Pressure or Isobaric Process

In this process, the system is maintained at constant pres￾sure and any transfer of heat would result in work done by

the system or on the system.

2.0.6.3 Enthalpy

The sum of internal energy and pressure volume product

(i.e., U þ pV ) is known as enthalpy and is denoted by H.

As both U, p, and V are known as system properties,

enthalpy is also a system property.

2.0.6.4 Constant Temperature of the Isothermal

Process

The system is maintained at a constant temperature by any

means and an increase in volume would result in a decrease

in pressure and vice versa.

Introduction Chapter | I 3

2.0.7 Second Law of Thermodynamics

There is a limitation of the First Law of Thermodynamics,

as it assumes a reversible process. In nature there is actually

a directional law, which implies a limitation on the energy

transformation other than that imposed by the First Law of

Thermodynamics

Whenever energy transfers or changes from one system

to another are equal, there is no violation of the First Law of

Thermodynamics; however, that does not happen in prac￾tice. Thus, there must exist some directional law governing

transfer of energy.

2.0.8 Heat Engine

A heat engine is a cyclically operating system across whose

boundary is a cyclically operating system across which

only heat and work flow. This definition incorporates any

device operating cyclically and its primary purpose is

transformation of heat into work.

Therefore if boiler, turbine, condenser, and pump are

separately considered in a power plant, they do not stand

included in the definition of heat engines because in each

individual device in the system does not complete a cycle

(Figure I/2-1).

When put together, however, the combined system

satisfies the definition of a heat engine. Referring to

Figure I/2.1-1, the heat enters the boiler and leaves at the

condenser. The difference between these equals work at

the turbine and pump. The working medium is water and it

undergoes a cycle of processes. Passing through the boiler

and transforming to steam, it goes to the turbine and then

to the condenser where it changes back into water and goes

to the feed pump, and finally to the boiler again to its initial

state.

2.0.8.1 Kelvin Planck Statement of the Second

Law of Thermodynamics

It is impossible to construct an engine that while operating

in a cycle produces no other effect except to extract heat

from a single reservoir and do the equivalent amount of

work. Thus, it is imperative that some heat be transferred

from the working substance to another reservoir, or cyclic

work is possible only with two temperature levels involved

and the heat is transferred from a high temperature to a heat

engine and from a heat engine to a low temperature.

2.0.8.2 Clausius Statement of the Second Law of

Thermodynamics

“It is impossible for heat energy to flow spontaneously

from a body at lower temperature to a body at higher

temperature.”

2.1 Recapitulation: Various Cycles: Carnot,

Rankine, Regenerative, and Reheat

2.1.1 Reversible Cycle: Carnot

Here a reversible cycle was proposed by Sadi Carnot, the

inventor of this it, in which the working medium receives

heat at one temperature and rejects heat at another tem￾perature. This is achieved by two isothermal processes and

two reversible adiabatic processes, shown in the simplified

schematic in Figure I/2.1-1.

A given mass of gas (system) is expanded isothermally

from point 1 at temperature T1 to point 2 (after receiving

heat q1 from an external source). So, work is done by the

system. The system is now allowed to expand further to

point 3 at temperature T2 through a reversible adiabatic

FIGURE I/2-1 Power plant as basic heat engine. FIGURE I/2.1-1 p-v diagram of a Carnot (reversible) cycle.

4 POWER PLANT INSTRUMENTATION AND CONTROL HANDBOOK

process, meaning no exchange of heat or transfer except

work is done due to expansion.

Now the system at point 3 is allowed to reject heat q2 to

a sink at temperature T2 isothermally up to point 4 by

compressing (i.e., doing work on the system). At point 4,

the system is again compressed up to point 1, the starting

point, through a reversible adiabatic process (i.e., without

any heat transfer). Now because the system has completed

a cycle and returned to initial state, its internal energy

remained the same, as per the First Law of Thermody￾namics. Now, q1 q2 ¼ W ¼ work done.

2.1.2 Application of Carnot Cycle in Power

Plant

The previous schematic in Figure I/2.1-1 is a classical

demonstration of the Carnot cycle. The watere

steam flow cycle of a steam power plant is shown in

Figure I/2.1-2.

Here the isothermal process or heat transfers take place

in the boiler at temperature T1 and in the condenser at

temperature T2. In these two operations, the fluid is under￾going change in phase; in other words, in the boiler water is

transformed to steam at temperature T1 and in the condenser,

steam is transformed into water at temperature T2.

The reversible adiabatic expansion is performed at the

turbine and reversible adiabatic compression takes place in

the (boiler) feed pump.

2.1.3 Carnot Theorem or Corollary 2

No engine working between two temperatures can be more

efficient than the reversible engine working between the

same two temperatures or the Carnot engine (hypothetical).

Among all engines operating between fixed temperatures, it

is the most efficient.

2.1.4 Properties of Steam

Water is introduced into the boiler by a feed pump at a

certain pressure and temperature adding some energy to the

system. At the boiler, heat is added to raise the temperature

at a saturation temperature corresponding to that initial

pressure. This is called “sensible heat,” as the rise in tem￾perature is evident. When the saturation stage is attained,

further addition of heat would change the phase of water to

steam without a temperature rise but a sensible change in

volume. This stage would continue until dry saturation

steam is available. As there is no change in temperature, the

heat added is called “latent heat” and is denoted by L.

2.1.4.1 Steam Table

Normally the properties of steam include different param￾eters, such as pressure, temperature, volume, enthalpy,

entropy, etc., and their interrelations are experimentally

determined and presented in a tabular form. These values

are referred to and required values are obtained from

reference tables instead of calculating from the equations,

which are very complex.

2.1.4.2 Wet Steam

Wet steam may be described as steam with a mixture of

liquid water and water vapor suspended in it. The fraction

of steam present in the mixture by weight is called the

dryness fraction of steam.

2.1.4.3 Superheated Steam

Superheated steam behavior is like a perfect gas; the vol￾ume of a given mass can be determined by the Charles Law

(i.e., p is constant). All the properties of superheated steam

are normally found in reference steam tables, the figures of

which were found by performing experiments to explain

variations in specific heat and other influencing factors.

2.1.4.4 Entropy

It can be proved that the integral value of change in heat

transfers divided by temperature in a cyclic path is equal to

zero.

Cyclic Z

ðvq=TÞrev ¼ 0

or

ðvQ=TÞ ¼ dS;

where S is called entropy, or change in entropy during a

reversible process can be written as follows:

Z2

1

ðvQ=TÞrev ¼

Z2

1

dS ¼ ðs2 s1Þ ¼ DS

FIGURE I/2.1-2 Wateresteam simplified flow cycle of a power plant.

Introduction Chapter | I 5

For unit mass, Z 2

1

ðvq=TÞrev ¼

Z 2

1

ds ¼ Ds

2.1.4.4.1 Corollary 5 Corollary 5 of the Second Law of

Thermodynamics indicates that there exists a property

called entropy of a system such that for a reversible process

from point 1 to point 2 in a process path, its change is given

as

Z2

1

ðvQ=TÞrev for a unit mass

Therefore it is evident that entropy is not a path function

but a point function and change of entropy can be

shown as:

ds ¼ ðdU þ pdVÞ=T

or, in another way,

Tds ¼ dU þ pdV

This equation is very important as it is evident that the

relationships among all parameters are thermodynamic

properties and not path functions such as heat or work. It is

interesting that the equation

Tds ¼ dU þ pdV

is applicable to both reversible and irreversible processes,

but

vQ ¼ Tds and vQ ¼ dU þ pdV

are only applicable to reversible process.

2.1.5 TemperatureeEntropy Diagram

As it is known that 1Q ¼

Z s2

s1

Tds, it can be graphically

realized as the area under the curve with temperature and

entropy as the coordinates as seen in Figure I/2.1-3.

Figure I/2.1-4 also graphically represents the work done in

a separate set of pressure and volume coordinates; for

example, work done in these coordinates is

1W2 ¼

Zv2

v1

pdv

By the First Law of Thermodynamics:

Cyclic Z

vQ ¼

Z

dW

(i.e., heat transferred to the system is equal to the work

done by system). From the previous equation, a very impor￾tant conclusion can be drawn: the “enclosed area for a

reversible cyclic process represents work done by heat

transfers on both peV as well as Tes coordinates. Thus,

in the Carnot cycle represented on the peV or Tes coordi￾nates, the enclosed area denotes work done or heat

transfers. From various logical derivations and approxima￾tions, it can be said that for an irreversible process, entropy

change is not equal to (vQ/T), but more than (vQ/T); in

other words, the (ds) isolated system is 0, which is known

as Corollary 6 of the Second Law of Thermodynamics.

2.1.6 Entropy of Different Phases of Water

and Steam

2.1.6.1 Entropy of Water

By definition, ds ¼ dq/T ¼ Cp. dT/T; therefore,

ðs2 s1Þ ¼ Z T2

T1

Cp dT=T ¼ Cp loge T2=T1 If 0C or

FIGURE I/2.1-3 Temperatureeentropy diagram of reversible process.

FIGURE I/2.1-4 Pressure volume diagram of reversible process.

6 POWER PLANT INSTRUMENTATION AND CONTROL HANDBOOK

273 K is chosen as the datum for entropy, then entropy of

water at any temperature T would be s ¼ Cp loge T/273 and

entropy of water at saturation temperature Ts is sw ¼ Cpw

loge Ts/273.

2.1.6.2 Entropy of Steam

Heat required to convert a unit mass of water to a unit mass

of dry saturated steam is the latent heat of vaporization and

is denoted by L. Therefore, sL ¼ L/Ts, or, the entropy of

vaporization of wet steam is xSL ¼ xL/Ts, where x ¼ dry￾ness fraction of steam; in other words, it is the fraction of

dry saturation steam to total mass of the steam. Entropy of

dry saturated steam is given by the following:

s ¼ sw þ sL ¼ Cpw logeTs

273 þ xL

Ts:

2.1.6.3 Entropy of Superheated Steam

For unit mass of dry saturated steam to get superheated to

temperature Tsup at constant pressure, the entropy excursion

may be given as follows:

ssup ss ¼

Z

Tsup

Ts

Cp:dTsup=Ts ¼ CplogeTsup

Ts:

Therefore, the entropy of superheated steam may be

expressed as follows:

ssup ¼ Cpw logeTs=273 þ L=Ts þ Cp logeTsup

Ts:

These equations are very cumbersome and are not used

much because these entropy values can be found in refer￾ence steam tables.

2.1.7 TemperatureeEntropy Diagram

of Steam

From the equation sw ¼ Cpw loge Ts/273, different values of

saturation temperature are plotted against values of entropy

at different pressures (see Figure I/2.1-5).

In this figure, the portion of graph from point 1 to 2 is

considered the water or liquid line. From point 2 to point 3,

the path is a straight horizontal line at constant saturation

temperature Ts denoting the water and vapor mixture phase.

At point 3, the dry saturation stage is achieved. From point

3, if the process follows path 3e4, then different values of

dry saturated temperatures are available at lower saturation

pressure up to point 4. These two lines or paths when

plotted for higher pressure corresponding to a higher

saturation temperature would finally merge at point C,

which is called the critical point. Here the saturation tem￾perature is 374.065C and pressure is 225.415 kgf/cm2

. At

this point water transforms into the gaseous phase (i.e., dry

saturation steam) directly without passing through the two￾phase system, and the latent heat of vaporization is zero.

In path 3e4, at any point, if the steam is further heated

at constant pressure, the process will follow path 3e5 or

6e7 up to the temperatures of superheated steam corre￾sponding to heat added. After this the region is denoted as a

superheat region.

2.1.7.1 PressureeVolume Diagram

The pressureevolume diagram corresponding to the tem￾peratureeentropy diagram is illustrated in Figure I/2.1-6.

The critical point C is at 225.415 kgf/cm2

. Liquid, wet,

and superheat regions are depicted; 1e2 and extension up

to point C is the water line. Line 3e4 and extension up to

point C is the dry saturation line. Constant pressure heating

is represented by 1e2e3e5.

FIGURE I/2.1-5 Temperatureeentropy diagram of steam.

FIGURE I/2.1-6 Pressureevolume diagram of steam.

Introduction Chapter | I 7